Dolbeault dga and L_∞-algebroid of the formal neighborhood

We continue the study the Dolbeault dga of the formal neighborhood of an arbitrary closed embedding of complex manifolds previously defined by the author in [14]. The special case of the diagonal embedding has been analyzed in [13]. We describe here the Dolbeault dga of a general embedding explicitly in terms of the formal differential geometry of the embedding. Moreover, we show that the Dolbeault dga is the completed Chevalley-Eilenberg dga of an L_∞-algebroid structure on the shifted normal bundle of the submanifold. This generalizes the result of Kapranov on the diagonal embedding and Atiyah class.